Respuesta :
Answer:
SD = 10.1
Step-by-step explanation:
We have been given that Kori knows that the mean of the data is 120 and that 84% of the data values are less than 130.
We will use z-score formula to find standard deviation of our given data set.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z[/tex] = z-score,
[tex]x[/tex] = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Let us find z-score corresponding to the area of population under curve less than 84%.
From normal distribution table we get that z-score corresponding to area less than 84% is 0.99.
Upon substituting our given values in z-score formula we will get,
[tex]0.99=\frac{130-120}{\sigma}[/tex]
[tex]0.99=\frac{10}{\sigma}[/tex]
[tex]\sigma=\frac{10}{0.99}[/tex]
[tex]\sigma=10.101010\approx 10.1[/tex]
Therefore, the standard deviation of our given data set is 10.1.
